scholarly journals A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Rui Li ◽  
Pengcheng Wang ◽  
Yu Tian ◽  
Bo Wang ◽  
Gang Li
Keyword(s):  
Free Vibration ◽  
Analytic Solution ◽  
Thin Plates ◽  
Solution Approach ◽  
Vibration Problems

Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method

2020 ◽  
pp. 107754632096782
Author(s):  
Xin Su ◽  
Eburilitu Bai
Keyword(s):  
Free Vibration ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Superposition Method ◽  
Elastic Foundations ◽  
Vibration Problem ◽  
Separation Variable ◽  
Vibration Problems ◽  
Two Parameter ◽  
Free Edges

The free vibration of orthotropic rectangular thin plates with four free edges on two-parameter elastic foundations is studied by the symplectic superposition method. Firstly, by analyzing the boundary conditions, the original vibration problem is converted into two sub-vibration problems of the plates slidingly clamped at two opposite edges. Based on slidingly clamped at two opposite edges, the fundamental solutions of these two sub-vibration problems are respectively derived by the separation variable method of the corresponding Hamiltonian system, and then the symplectic superposition solution of the original vibration problem is obtained by superimposing the fundamental solutions of the two sub-problems. Finally, the symplectic superposition solution obtained in this study is verified by calculating the frequencies and mode functions of several concrete rectangular thin plates with four free edges.

scholarly journals Application of Laplace Transform to the Free Vibration of Continuous Beams

2017 ◽  
Vol 63 (1) ◽  
pp. 163-180 ◽  
Author(s):  
H.B. Wen ◽  
T. Zeng ◽  
G.Z. Hu
Keyword(s):  
Free Vibration ◽  
Laplace Transform ◽  
Reaction Force ◽  
Bending Moment ◽  
Frequency Equation ◽  
Simplified Model ◽  
Continuous Beam ◽  
Transform Method ◽  
Continuous Beams ◽  
Vibration Problems

AbstractLaplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.

Static Deflection and Free Vibration of Nonprismatic Beam Structures Solved by DQEM Using EDQ

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Equilibrium Equation ◽  
Static Deflection ◽  
Beam Structures ◽  
Prismatic Beam ◽  
Vibration Problems ◽  
Analysis Models ◽  
Element Boundary

Abstract The development of (DQEM) analysis models of static deformation and free vibration problems of generic non-prismatic beam structures was carried out. The DQEM uses the extended differential quadrature (EDQ) to discretize the buckling equilibrium equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. They prove that the DQEM efficient.

New analytic free vibration solutions of rectangular thin plates resting on multiple point supports

2016 ◽  
Vol 110 ◽  
pp. 53-61 ◽  
Author(s):  
Rui Li ◽  
Yu Tian ◽  
Pengcheng Wang ◽  
Yunfeng Shi ◽  
Bo Wang
Keyword(s):  
Free Vibration ◽  
Thin Plates ◽  
Multiple Point

scholarly journals Green’s function approach to frequency analysis of thin circular plates

2016 ◽  
Vol 64 (1) ◽  
pp. 181-188
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Influence Function ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Circular Plates ◽  
Natural Modes ◽  
Good Agreement ◽  
Analytical Frequency

Abstract The free vibration analysis of homogeneous and isotropic circular thin plates by using the Green’s functions is considered. The formulae for construction of the influence function for all nodal diameters are presented in a closed form. The limited independent solutions of differential Euler equations were expanded in the Neumann power series using the method of successive approximation. This approach allows to obtain the analytical frequency equations as power series rapidly convergent to exact eigenvalues for different number of nodal diameters. The first ten dimensionless frequencies for eight different natural modes of circular plates are calculated. A part of obtained results have not been presented yet in open literature for thin circular plates. The results of investigation are in good agreement with selected results obtained by other methods presented in literature.

FREE VIBRATION ANALYSIS OF NON-UNIFORM TIMOSHENKO BEAMS USING DIFFERENTIAL TRANSFORM

1998 ◽  
Vol 22 (3) ◽  
pp. 231-250 ◽  
Author(s):  
Cha’o Kuang Chen ◽  
Shing Huei Ho
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Present Method ◽  
Series Solution ◽  
Free Vibration Analysis ◽  
Timoshenko Beams ◽  
Differential Transform ◽  
Vibration Problems ◽  
Algebraic Operations

This study introduces using differential transform to solve the free vibration problems of a general elastically end restrained non-uniform Timoshenko beam. First, differential transform is briefly introduced. Second, taking differential transform of a non-uniform Timoshenko beam vibration problem, a set of difference equations is derived. Doing some simple algebraic operations on these equations, we can determine any i-th natural frequency, the closed form series solution of any i-th normalized mode shape. Finally, three examples are given to illustrate the accuracy and efficiency of the present method.

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